1. Field of the Invention
The present invention generally relates to non-linear optical devices and, more particularly, to a non-linear optical device that uses quantum dots.
2. Description of the Related Art
A non-linear optical device is an optical device that changes an optical state such as a refractive index or polarization plane thereof, in response to an electric field or optical radiation applied thereto. Thus, intensive and extensive investigations are being made on non-linear optical devices in relation to optical integrated circuits and optical information processing devices including photonic interconnection substrates, photonic multichip modules, photonic backplanes, and the like. Particularly, the non-linear optical devices are studied intensively in relation to an optical switch of an optical waveguide, an optical spatial modulator, an optical filter, and the like. In the case of an optical switch, for example, the optical path of an optical beam passing through a non-linear optical medium is modified by inducing a change of refractive index in the medium by applying thereto a control optical beam or control electric field.
Conventionally, non-linear optical devices generally have used an inorganic crystal that lacks point symmetry, such as a LiNbO.sub.3 crystal, for the non-linear optical medium. On the other hand, there is a proposal to use an organic polymer material having a substantially one-dimensionally aligned chain-like molecular structure for the material that shows a large non-linear optical effect. See for example T. Yoshimura, Fujitsu Sci. Tech. J., 27, 1, pp. 115-131, 1991. It should be noted that such a polymer that has a substantially one-dimensionally aligned molecular structure forms a quantum wire in which carriers are confined two-dimensionally. As a result of such a two-dimensional carrier confinement pertinent to a quantum wire, the polymer material shows a very large non-linear optical effect.
It should be noted that a non-linear optical effect is a result of mixing of different quantum states. Thus, the observed non-linear optical effect changes depending upon a difference as well as a degree of overlapping of the wavefunctions of different quantum states or quantum levels. For example, the susceptivity .beta. of a second-order non-linear optical effect is given by EQU .beta.=f.multidot.(P.sub.e -P.sub.g)
where the terms f, P.sub.e and P.sub.g are given as EQU f.varies.&lt;E.vertline.r.vertline.G&gt;.sup.2 EQU P.sub.e =&lt;E.vertline.r.vertline.E&gt;and P.sub.g =&lt;G.vertline.r.vertline.G&gt;,
in which the term f is an oscillator intensity while the terms P.sub.g and P.sub.e represent a dipole moment. In the foregoing representation, G stands for a wavefunction of a ground state and E stands for a wavefunction of an excited state. Further, r stands for a positional vector.
FIG. 1 shows the examples of calculated terms f, P.sub.e -P.sub.g and .beta. for three different sets of electron clouds corresponding to the wavefunctions E and G.
Referring to FIG. 1, it will be understood that the term P.sub.e -P.sub.g becomes zero when the wavefunctions E and G are identically located, as represented in the example at the left of FIG. 1. In such a case, therefore, no second-order non-linear optical effect is observed. When the difference between the wavefunctions E and G is excessive and there is no overlapping of the wavefunctions at all as in the example at the right of FIG. 1, the term f becomes substantially zero and the second-order non-linear optical effect .beta. is not observed. When the overlapping of the wavefunctions E and G is optimum as in the case at the center of FIG. 1, on the other hand, the foregoing term .beta. indicative of the second-order non-linear optical effect becomes a maximum.
As explained already, it is possible to maximize the second-order non-linear optical effect by using an organic material that includes a one-dimensionally extending quantum wire. Thus, it is predicted that the second-order non-linear optical effect would be enhanced further when quantum dots that confine carriers three-dimensionally is used for the non-linear optical medium of the non-linear optical device. Such quantum dots can be formed easily in an organic material in the form of discrete molecules.
However, such organic quantum dots generally fail to provide a desired sharp spectrum expected for a quantum dot due to the increased electron-photon interaction in an organic material. Thus, the enhancement of the second-order non-linear optical effect, which is based on the resonant excitation of electrons from the ground state G to the excited state E, is not achieved as desired when an organic quantum dot is used. Further, such an organic quantum medium tends to suffer from a problem in that the desired alignment of the molecules is difficult.
In a strained heteroepitaxial system as in a case of an InAs/GaAs epitaxial structure, on the other hand, it is also known that the quantum dots can be formed easily in the form of mutually isolated islands, by using a so-called S-K (Stranski-Krastanov) mode growth that appears in the initial period of a heteroepitaxial process. For example, there is a report that an island of InGaAs is formed on a GaAs substrate with a diameter of 30-40 nm, by depositing an InGaAs layer containing about 50% of. In on a GaAs substrate by an MBE process with a thickness of several molecular layers (Leonard, D., et al., Appl. Phys. Lett., 63, pp.3203-3205, 1993). Further, a similar formation of islands of InGaAs on a GaAs substrate is reported, in which the InGaAs islands are formed on the substrate by an ALE (atomic layer epitaxy) process with a diameter of 15-20 nm and a mutual separation of about 100 nm (Mukai, K., et al., Jpn. J. Appl. Phys., 33, pp.L1710-1712, 1994). Further, it is known that similar quantum dots can be formed also by using an MOVPE (metal-organic vapor phase epitaxy) process (Oshinowo, J., et al., Appl. Phys. Lett., 65(11), pp.1421-1423, 1994). Recently, self-assembled structures of closely stacked InAs islands grown on GaAs by an MBE process is reported by Nakata, et al., J. Crystal Growth 175/176 (1997), pp.713-719.
As the formation of the quantum dots in such a strained heteroepitaxial system is controlled by a strain induced at the heteroepitaxial interface, the formation of the quantum dots is much easier than the conventional process of forming a semiconductor quantum dot structure. In addition, the foregoing process is advantageous in the point that there is no need for conducting a patterning process such as an electron-beam lithography for forming the quantum dots, and that the quantum dots thus formed are substantially free from damage.
Therefore, it may be thought advantageous to use the heteroepitaxial semiconductor quantum dots thus formed on a semiconductor substrate for the non-linear optical medium of a non-linear optical device. In the quantum dots thus formed on a semiconductor substrate, the problem of electron-photon interaction is substantially suppressed as compared with the case of the quantum dots that use organic molecules.
However, conventional quantum dots, including those formed by the foregoing S-K mode, are not well controlled asymmetrically about a point of inversion (inversion asymmetry) and thus cannot be used effectively for a device that uses a second-order non-linear optical effect such as Pockels effect. As is well known in the art, the medium should not have a point symmetry or inversion symmetry in order to show a second-order non-linear optical effect. Thus, such conventional quantum dots cannot be used for devices that use a large non-linear optical effect such as an optical switch of an optical waveguide, an optical spatial modulator, optical filter or an optical modulator.